Class:
Name:
(
) Date:
Experiment 2d
2d Equivalent resistance of resistors in
series
Objective
To find out how the equivalent resistance of resistors connected in
series is related to the individual resistances of them.
Background information
1
or
2
The resistance of a conductor is defined as:
voltage across conductor
Resistance =
current through conductor
R=
V
I
By measuring the current I through a conductor when a known
voltage V is applied across it, the resistance of the conductor
V
can be determined from the formula R = .
I
Apparatus
❏ several carbon resistors of different resistance (including two 10-Ω resistors)
❏ 1 voltmeter
❏ 1 ammeter
❏ 1 battery box
❏ 1 switch
❏ several connecting leads
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© Oxford University Press 2007
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Experiment 2d
Class:
Name:
) Date:
Procedure
✐ The resistance of
a carbon resistor is
indicated by the colour
of the rings. Visit the
website http://www.
csgnetwork.com/
resistcolcalc.html to find
out how to calculate
the resistance from the
colour codes.
(
1
Set up the apparatus as shown in Figure 2d-1:
(a) Connect two 10-Ω resistors (R1 and R2) in series with an
ammeter, a 3-V battery box and a switch.
(b) Connect a voltmeter across the two resistors.
✐ Carbon resistors of
10 Ω and 100 Ω can be
found in Westminster
electromagnetic kit.
battery box
✐ The e.m.f. of
ammeter
the battery and the
resistances of the
resistors can be changed
to other values available.
switch
voltmeter
10-8 resistor
A
10-8 resistor
R1 = 10 8
R2 = 10 8
V
Fig 2d-1
30
2
(a) Measure the current I of the circuit using the ammeter and the
voltage V across the two resistors using the voltmeter.
(b) Record the results in Table 2d-1 on p.31 and calculate the
New Physics at Work (Second Edition)
V
I
ratio of the two resistors. This ratio is the equivalent resistance
Req of the two resistors.
© Oxford University Press 2007
Class:
Name:
(
Experiment 2d
) Date:
3
Repeat with other combinations of V, R1 and R2. Record the results in
Table 2d-1 and calculate the equivalent resistance Req.
✎
Results:
Equivalent
resistance
Resistance of
resistor R1 / Ω
Resistance of
resistor R2 / Ω
Voltage across
two resistors
V/V
Current of
circuit I / A
10
10
2.5
0.13
19..2
10
20
2.6
0.09
28.9
10
100
2.6
0.025
104.0
20
100
2.7
0.022
122.7
100
100
2.9
0.014
207.1
(Req =
V
)/Ω
I
Table 2d-1
✐ In this set of sample data, when a 100-Ω resistor is connected, the current is too small
to be measured by an ammeter and a multimeter. Therefore, it is better to use resistors with
resistances in a smaller range.
Discussion
✎
How is the equivalent resistance Req of the two resistors related to the
individual resistances R1 and R2 of them?
After allowing for errors, Req is equal to R1 + R2.
The equivalent resistance of resistors connected in series is equal
sum
to the ________________________
of the individual resistances of
them.
New Physics at Work (Second Edition)
© Oxford University Press 2007
31
Experiment 2d
Class:
Name:
(
) Date:
Further thinking
✎
By considering the current and voltage of each of the two resistors
connected in series, derive the relationship between the equivalent
resistance Req and the individual resistances R1 and R2 of them
mathematically. What will be the relationship if more resistors are
connected in series?
Voltage across R1: V1 = IR1
Voltage across R2: V2 = IR2
Total voltage across the two resistors: V = IReq
Since total voltage across the two resistors is equal to the sum of voltages across
each resistor:
V = V1 + V2
⇒ IReq = IR1 + IR2
⇒ Req = R1 + R2
If more resistors are connected in series, the equivalent resistance will still be equal
to the sum of the individual resistances of them.
32
New Physics at Work (Second Edition)
© Oxford University Press 2007